Can't get procedural displacement to work at all
The property you need to change is rather hidden in the UI unfortunately. Blender allows you to change the behavior of Displacement vector inputs per material. So as a result, there is a dropdown box in the Materials tab in the Properties Editor, under Settings -> Surface -> Displacement:



By default that will be set to Bump Only. Change it either to Displacement - which will displace the geometry - or Displacement and Bump, which will first displace the geometry and then apply the same texture as a bump map on top of that. Result looks like this in your file:



Second, in case you want to go really high with the level of detail, you'll need to enable the Experiental feature set to get Adaptive tessellation. Adaptive tessellation (sometimes called Microdisplacement) will give you more geometric details in areas when needed. Here's where to enable it first:



And here is the checkbox that needs to be enabled in each SubSurf modifier where you want adaptive displacement to kick in:



If you now render, you can see that the detail is a lot smoother, simply because now there are far more triangles in the mesh than before to capture the displacement detail: